THERMODYNAMICS
1. INTRODUCTION
In this topic we will study about thermal energy. In winter, when we rub our palms together, we feel warmer; here work done in rubbing produces the ‘heat’. Conversely, in a steam engine, the ‘heat’ of the steam is used to do useful work in moving the pistons, which in turn rotate the wheels of the train. In physics, we need to define the notions of heat, temperature, work, etc. more carefully.
Historically, it took a long time to arrive at the proper concept of ‘heat’. Before the modern picture, heat was regarded as a fine invisible fluid filling in the pores of a substance. On contact between a hot body and a cold body, the fluid (called caloric) flowed from the colder to the hotter body ! This is similar to what happens when a horizontal pipe connects two tank containing water up to different heights. The flow continues until the levels of water in the two tanks are the same. Likewise, in the ‘caloric’ picture of heat, heat flows until the ‘caloric levels’ (i.e., the temperatures) equalise.
In time, the picture of heat as a fluid was discarded in favour of the modern concept of heat as a form of energy. An important experiment in this connection was due to Benjamin Thomson (also known as Count Rumford) in 1798. He observed that boring of a brass cannon generated a lot of heat, indeed enough to boil water. More significantly, the
amount of heat produced depended on the work done (by the horses employed for turning the drill) but not on the sharpness of the drill.
In the caloric picture, a sharper drill
would scoop out more heat fluid from the pores; but this was not observed. A most natural explanation of the observations was that heat was a form of energy and the experiment demonstrated conversion of energy from one form to another–from work to heat.
Thermodynamics is the branch of physics that deals with the concepts of heat and whole temperature and the inter-conversion of heat and other forms of energy. Thermodynamics is a macroscopic science. It deals with bulk systems and does not go into the molecular constitution of matter. In fact, its concepts and laws were formulated in the nineteenth century before the molecular picture of matter was firmly established. Thermodynamic description involve relatively few macroscopic
variables of the system, which are suggested by common sense and can be usually measured directly. A microscopic description of a gas, for example, would involve specifying the co-ordinates and velocities of the huge number of molecules constituting the gas. The description in kinetic theory of gases is not so detailed but it does involve molecular distribution of velocities.
Thermodynamic description of a gas, on the other hand, avoids the molecular description altogether. Instead, the state of a gas in thermodynamics is specified by macroscopic variables such as pressure, volume, temperature, mass and composition that are felt by our sense perceptions and are measurable.
Thermodynamics is not concerned with the motion of the system as a whole. It is concerned with the internal macroscopic state of the body. When a bullet is fired from a gun, what changes is the mechanical state of the bullet (its kinetic energy, in particular), not its temperature. When the bullet pierces a wood and stops, the kinetic energy of the bullet gets converted into heat, changing the temperature of the bullet and the surrounding layers of wood. Temperature is related to the energy of the internal (disordered) motion of the bullet, not to the motion of the bullet as a whole.
2. THERMAL EQUILIBRIUM
Equilibrium in mechanics means that the net
external force and torque on a system are zero. The term ‘equilibrium’ in thermodynamics appears
in a different context : we say the state of a system is an equilibrium state if the macroscopic variables that characterise the system do not change in time. For example, a gas inside a closed rigid container,completely insulated from its surroundings, with fixed values of pressure, volume, temperature, mass and composition that do not change with time, is in a state of thermodynamic equilibrium.
In general, whether or not a system is in a state
of equilibrium depends on the surroundings and
the nature of the wall that separates the system from the surroundings. Consider two gases A and B occupying two different containers. We know experimentally that pressure and volume of a given mass of gas can be chosen to be its two independent variables. Let the pressure and volume of the gases be (PA , V A ) and (P B , VB ) respectively. Suppose first that the two systems are put in proximity but are separated by an adiabatic wall – an insulating wall (can be
movable) that does not allow flow of energy (heat) from one to another. The systems are insulated from the rest of the surroundings also by similar adiabatic walls. The situation is shown schematically. In this case, it is found that any possible pair of values (PA , V A ) will be in equilibrium with any possible pair of values (P B
, VB ). Next, suppose that the adiabatic wall is replaced by a diathermic wall – a conducting wall that allows energy flow (heat) from one to another. It is then found that the macroscopic variables of the systems A and B change spontaneously until both the systems attain equilibrium states. After that there is no change in their state. The pressure and volume variables of the two gases change to (P B ′, VB ′) and (PA ′, V A ') such that the new states of A and B are in equilibrium with each other. There is no more energy flow from one to another.
We then say that the system A is in thermal
equilibrium with the system B.
What characterises the situation of thermal equilibrium between two systems ? You can guess the answer from your experience. In thermal equilibrium, the temperatures of the two systems are equal. We shall see how does one arrive at the concept of temperature in thermodynamics? The Zero t h law of thermodynamics provides the clue. ZERO T H LAW OF THERMODYNAMICS. It is found that the states of A and B change no further i.e. they are found to be in thermal equilibrium with each other. This observation forms the basis of the Zero t h Law of Thermodynamics, which states that ‘two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other’. R.H. Fowler formulated this law in 1931 long after the first and second Laws of thermodynamics were stated and so numbered.
3. The zero t h law
The Zero t h Law clearly suggests that when two
systems A and B, are in thermal equilibrium, there must be a physical quantity that has the same value for both. This thermodynamic variable whose value is equal for two systems in thermal equilibrium is called temperature (T ).
Thus, if A and B are separately in equilibrium with C, TA = TC and TB = TC. This implies that TA = TB i.e. the systems A and B are also in thermal equilibrium. We have arrived at the concept of temperature formally via the Zero t h Law. Thermometry deals with this basic question to which we turn in the next section.
4. HEAT, INTERNAL ENERGY AND WORK
The Zero t h Law of Thermodynamics led us to the concept of temperature that agrees with our commonsense notion. Temperature is a marker of the ‘hotness’ of a body. It determines the direction of flow of heat when two bodies are placed in thermal contact. Heat flows from the body at a higher temperature to the one at lower temperature. The flow stops when the temperatures equalise; the two bodies are then in thermal equilibrium. We saw in some detail how to construct temperature scale to assign temperatures to different bodies. We now describe the concepts of heat and other relevant quantities like internal energy and work. The concept of internal energy of a system is not difficult to understand. We know that every bulk system consists of a large number of molecules. Internal energy is simply the sum of the kinetic energies and potential energies of these molecules. We remarked earlier that in thermodynamics, the kinetic energy of the system, as a whole, is not relevant. Internal energy is thus, the sum of molecular kinetic and potential energies in the frame of reference relative to which the centre of mass of the system is at rest. Thus, it includes only the (disordered) energy associated with the random motion of molecules of the system. We denote the internal energy of a system by U.
Though we have invoked the molecular
picture to understand the meaning of internal energy, as far as thermodynamic is concerned,U is simply a macroscopic variable of the system. The important thing about internal energy is that it depends only on the state of the system, not on how that state was achieved. Internal energy U of a system is an example of a thermodynamic ‘state variable’ – its value depends only on the given state of the system,not on history i.e. not on the ‘path’ taken to arrive at that state. Thus, the internal energy of a given mass of gas depends on its state described by specific values of pressure, volume and temperature. It does not depend on how this state of the gas came about. Pressure, volume, temperature, and internal energy are thermodynamic state variables of the system (gas) . If we neglect the small intermolecular forces in a gas, the internal energy of a gas is just the sum of kinetic energies associated with various random motions of its molecules. In a gas this motion is not only translational (i.e. motion from one point to another in the volume of the container); it also includes rotational and vibrational motion of the molecules .
5. HEAT ENGINES
Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat to work.
» It consists of a working substance–the
system. For example, a mixture of fuel
vapour and air in a gasoline or diesel engine or steam in a steam engine are the working substances.
» The working substance goes through a cycle consisting of several processes. In some of these processes, it absorbs a total amount of heat Q 1from an external reservoir at some high temperature T1.
» In some other processes of the cycle, the
working substance releases a total amount of heat Q 2 to an external reservoir at some lower temperature T2.
» The work done (W ) by the system in a cycle is transferred to the environment via some arrangement (e.g. the working substance may be in a cylinder with a moving piston that transfers mechanical energy to the wheels of a vehicle via a shaft).
Some important questions:
Question 1:
A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If
the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat
of combustion is 4.0 × 104 J/g?
Answer 1:
Water is flowing at a rate of 3.0 litre/minute.
The geyser heats the water, raising the temperature from 27°C to 77°C.
Initial temperature, T1 = 27°C
Final temperature, T2 = 77°C
Rise in temperature, Δ T = T2 – T1
= 77 – 27= 50°C
Heat of combustion = 4 × 104 J/g
Specific heat of water, c = 4.2 J g–1 °C–1
Mass of flowing water, m = 3.0
litre/minute = 3000 g / m in
ute
Total heat used, Δ Q = m c Δ T
= 3000 × 4.2 × 50
= 6.3 × 105 J/m in
ute
Rate of consumption = 6.3×10^5 /4×10^4= 15.75 g/minute.
Question 2:
In changing the state of a gas adiabatically from an equilibrium state A to another
equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)
Answer 2:
The work done (W) on the system while the gas changes from state A to state B is 22.3 J.
This is an adiabatic process. Hence, change in heat is zero.
Δ Q = 0
Δ W = –22.3 J (Since the work is done on the system)
From the first law of thermodynamics, we have:
Δ Q = Δ U + Δ W
Where,
Δ U = Change in the internal energy of the gas
Δ U = Δ Q – Δ W = – (– 22.3 J)
Δ U = + 22.3 J
When the gas goes from state A to state B via a process, the net heat absorbed by the
system is:
Δ Q = 9.35 cal = 9.35 × 4.19 = 39.1765 J
Heat absorbed, Δ Q = Δ U + Δ Q
Δ W = Δ Q – Δ U
= 39.1765 – 22.3
= 16.8765 J
Therefore, 16.88 J of work is done by the system.
More questions:
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